Question: Christopher is 3 years older than Daniel. Nine years ago, Christopher was 4 times as old as Daniel. How old is Daniel now?
Solution: We can use the given information to write down two equations that describe the ages of Christopher and Daniel. Let Christopher's current age be $c$ and Daniel's current age be $d$ The information in the first sentence can be expressed in the following equation: $c = d + 3$ Nine years ago, Christopher was $c - 9$ years old, and Daniel was $d - 9$ years old. The information in the second sentence can be expressed in the following equation: $c - 9 = 4(d - 9)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $d$ , it might be easiest to use our first equation for $c$ and substitute it into our second equation. Our first equation is: $c = d + 3$ . Substituting this into our second equation, we get the equation: $(d + 3)$ $-$ $9 = 4(d - 9)$ which combines the information about $d$ from both of our original equations. Simplifying both sides of this equation, we get: $d - 6 = 4 d - 36$ Solving for $d$ , we get: $3 d = 30$ $d = 10$.